Movie editing: low FPS on preview
Why does it happen?

There is a very simple explanation to this: to increase performance of various things (including video playback), Blender has a fixed-size cache in your RAM. Using this Blender preloads frames into quicker memory for faster playback (this is what you see for the ten first seconds.). When the cache fills, Blender starts doing the following:


Read the frame from the hard drive
Decode the frame
Push it to the cache (overwriting whatever was in the way)
Read it from the cache and draw it on screen.


This is slower because:


You are limited by the speed of your hard drive.
Decoding the frame takes time
Pushing things to the cache is an extra overhead.
The processing time used up by the above is taken away from actually playing back the video.


This explains the overall sluggishness.

How does one solve it?

You can adjust the size of the cache: in User Preferences > System > Memory Cache Limit. I personally advise using as much as you can manage. It also reduces the amount of crashes due to memory leaks (this is especially true on Windows). A bigger cache means a faster Blender in general.

Also, you can make Blender prefetch frames in the Clip Editor and Sequencer. Do this by going to User Preferences > System > Sequencer / Clip Editor. I hope this helps.

Also have a look at:


How to make VSE render faster?
http://blenderartists.org/forum/showthread.php?349186-Does-Blender-has-a-cache-size-limit-(per-frame)


[Edit]

If the codec is slow to decode, having frames cached is even more important.